## myininaya Group Title I have the following information: $n=p^2q$ $k \ge 4$ $0<v<n$ $0 \le x < pq$ $y=\lceil \frac{(v-x^k) \mod n}{pq} \rceil \cdot (kx^{k-1})^{-1} \mod p$ I want to show: $\sum_{i=0}^{k}\left(\begin{matrix} k \\ i \end{matrix}\right) x^{k-1}(ypq)^i \equiv x^k+kypqx^{k-1}$ the congruence is mod n 2 years ago 2 years ago

1. satellite73 Group Title

i can't even read this what class?

2. myininaya Group Title

i made a mistake $\sum_{i=0}^{k}\left(\begin{matrix} k \\ i \end{matrix}\right) x^{k-i}(ypq)^i \equiv x^k+kypqx^{k-1}$ I'm trying to follow a proof but i don't know how they got from that one part to the other part

3. satellite73 Group Title

yeah well i cannot read what it says. good luck

4. myininaya Group Title

http://www.cacr.math.uwaterloo.ca/hac/ its in chapter 11 on page 473 at the bottom

5. myininaya Group Title

;p;

6. myininaya Group Title

lol*

7. myininaya Group Title

i wonder if james or zarkon could do it

8. myininaya Group Title

oh its zarkon lol

9. satellite73 Group Title

good luck!

10. KingGeorge Group Title

ask me next semester when I've taken cryptography, and I might be able to help you, but right now, I haven't got a clue.

11. Zarkon Group Title

only the first two values of i will matter (i=0,1) for i>1 you have a $$(pq)^2$$ part which is $$p^2qq=nq$$ which is zero nod n

12. myininaya Group Title

i don't see this (pq)^2 part

13. myininaya Group Title

george what kind of math have you had?

14. Zarkon Group Title

${k\choose i}x^{k-1}(ypq)^i$ for $$i\ge2$$ ${k\choose i}x^{k-1}(ypq)^i={k\choose i}x^{k-1}(y^i)(pq)^{i-2}p^2qq$ $=\left({k\choose i}x^{k-1}(y^i)(pq)^{i-2}q\right)\times n$

15. myininaya Group Title

ok i see

16. myininaya Group Title

you are so smart to notice the first two values will only matter since n mod n is like totally 0 thanks zarkon

17. KingGeorge Group Title

I've only had a year and a half of college level math so far, so that means, calc 1-3, lin. algebra, abstract algebra, and analysis

18. Zarkon Group Title

no problem :)

19. myininaya Group Title

is there any number theory in abstract algebra i can't remember

20. KingGeorge Group Title

not very much. I'm taking intro to number theory, and cryptography next semester.

21. myininaya Group Title

i like cryptography

22. myininaya Group Title

number theory is so cool and interesting to me although my skills suck right now

23. KingGeorge Group Title

It certainly sounds fun. I'm definitely enjoying my abstract algebra class right now. We had the barest hints of some number theory in discrete math so I'm not completely helpless.

24. myininaya Group Title

i like these math puzzles

25. myininaya Group Title

differential equations is not as fun to me but i do like the remedial kind lol

26. myininaya Group Title

zarkon do you think there is hope for my brain?

27. KingGeorge Group Title

From my experience, I don't like differential equations very much. Granted, I've never had a full course in it, but it just isn't my thing.

28. Zarkon Group Title

there is!

29. myininaya Group Title

i feel like i'm trapped inside with an apes' brain

30. Zarkon Group Title

A very smart ape ;)

31. myininaya Group Title

thanks i take that as a compliment

32. Zarkon Group Title

If you want a fun class...Take a course in measure theoretic probability theory.

33. myininaya Group Title

he says that because he is a stat nerd

34. KingGeorge Group Title

I don't think my school has that class...

35. myininaya Group Title

my doesn't either

36. Zarkon Group Title

or a class in stochastic processes

37. Zarkon Group Title

sometimes it will fall under the title of applied probability

38. myininaya Group Title

i think they might have that

39. myininaya Group Title

i always had a 10 foot pole when it came to statistics i only had to put it down when the course in stat was required

40. KingGeorge Group Title

I'm personally more of an algebra person. Stats was interesting at first, but then it got boring.

41. myininaya Group Title

There are some cool things though in stat i do admit

42. Zarkon Group Title

There is plenty of really nice mathematics in statistics

43. KingGeorge Group Title

It was the same with calculus for me. Interesting at first, and then it just stopped interesting me.

44. Zarkon Group Title

A lot of multivariate calculus and matrix theory

45. myininaya Group Title

zarkon can i ask another question

46. myininaya Group Title

this is my last problem with this proof...

47. Zarkon Group Title

ok

48. myininaya Group Title

omg never i got it lol

49. myininaya Group Title

i mean nvm

50. myininaya Group Title

i was typing it all out then i realized oh yeah lol

51. Zarkon Group Title

ok :)

52. myininaya Group Title